Having watched many of these videos now, I have not seen any special bottle. Having a dispensing bottle is generally only required if you are buying your glue in large volume containers (5 liter for example). There are some bottles you can buy that allow you to fill from the top, but, rather like a teapot, you pour from the bottom.
I personally buy glue in smaller containers (I am not a pro woodworker). The best tip I have found however, is to get an old lid, or short piece of pipe or similar, and store the bottle upside down. That way, if the glue does start to skin up, it will do so on the bottom of the bottle, rather than the top, saving me from having to open the bottle to clean the nozzle and remove the skin.
I just use plain-ol’ Titebond II glue, in its original bottle. Keep it closed when not in use. May store it upside down when near empty. Only issue I have with skinning is sometimes from leftover glue on the tip. Just pull it off with my fingernail.